WASHINGTON — Senators on Wednesday rolled out competing plans for the nation’s health care system, with a group of GOP senators making a last, long-shot effort to undo President Barack Obama’s Affordable Care Act and independent Senator Bernie Sanders of Vermont proposing universal government-run coverage.

Despite opposition and little time, Senators Lindsey Graham, Republican of South Carolina, and Bill Cassidy, Republican of Louisiana, proposed legislation that would do away with many of the subsidies and mandates of the 2010 law and instead would provide block grants to the states to help individuals pay for health coverage.

‘‘If you believe repealing and replacing Obamacare is a good idea, this is your best and only chance to make it happen because everything else has failed except this approach,’’ Graham told reporters.

Advertisement

The senators said that some states would get more money to provide health care than they get through the current system. They are modeling their effort after the welfare reform legislation passed under President Bill Clinton in the 1990s. They said states are better equipped than Washington to determine how best to meet the needs of their residents.

President Trump lauded the senators’ efforts, but it was unclear how much energy the White House was actually putting into the health care drive with GOP attention shifting to a tax overhaul.

‘‘Inaction is not an option, and I sincerely hope that Senators Graham and Cassidy have found a way to address the Obamacare crisis,’’ Trump said.

Advertisement

The White House issued the statement after Graham used the news conference to urge Trump to ‘‘pick up the phone’’ and round up support from governors.

‘‘Tell them this matters to you, that you weren’t kidding about repealing and replacing Obamacare, that you actually meant it,’’ Graham said. ‘‘So Mr. President, help us because we’re trying to help you.’’

Graham and Cassidy have struggled for weeks to round up sufficient support for their package, although Senators Ron Johnson, Republican of Wisconsin, and Dean Heller, Republican of Nevada, signed on. It would cut and reshape Medicaid, disperse money spent under Obama’s law directly to states, and erase Obama’s penalties on people who don’t purchase coverage.

A third effort, a bipartisan attempt to shore up individual insurance markets around the country, is showing early signs that the sides are having problems reaching agreement.

Senators Lamar Alexander, Republican of Tennessee, and Patty Murray, Democrat of Washington, hope to reach a deal on continuing for at least a year the federal payments to insurers that Trump has threatened to halt. Republicans are also insisting on easing the Obama law’s coverage requirements, which Democrats oppose.